Where Do Rebounds Go?

Jul 18

Here’s a basic basketball question: if a player misses a 3-point shot from the left corner, where will the rebound go? The answer to this question has obvious competitive advantages, regardless of whether you are playing a pick-up game at the park or you are playing in the gold-medal game of the Olympics.

So what’s the answer? Where do missed corner 3′s end up? Thanks to SportVu data, we can now answer this question. I plotted and analyzed the rebounding locations for over 26,000 missed shots from the 2011-2012 NBA season, including about 1,800 missed corner 3′s. When an NBA player misses a corner 3 from his left side, the rebounds go here:

The spatial structure above is undeniable; missed corner 3′s go to the opposite side much more frequently than they ricochet back toward their origin. In fact, the most common location for a missed corner 3 rebound is just south of the college “low block” on the opposite side. Rebounds land there about 5X more often than they do at the corresponding location near the other block.

So, where do rebounds happen? It depends. It depends on shot location, rebounder positioning, and rebounder athleticism. In this article I examine the interactions between shot location and rebounding location in the NBA. I think I’ve found some interesting results that are likely to change the ways you think about rebounding and boxing out.

This interactive graphic reveals** where rebounds go according to shot location. As you mouse over different sections of the court, the rebounding signatures change:

** if you are on an iPad, iPhone, or some other device that does not support Flash, this will not work for you. Please check back from another device. I’ve also included other graphics below that will work for you non-Flash types.

I will provide much more detail later, but here are 4 main takeaways:

1. Rebounds go to “the other side” – when a field goal is attempted from the baseline or wing areas and it misses, chances are the rebound will occur on the opposite side of the rim. How much to the other side depends on where the shot was taken (shot angle, shot direction).

2. Offensive rebounding percentage for jump shots hovers between 20 and 25%; however, missed shots closer to the rim such as floaters, put-backs, and layups result in a much higher offensive rebounding rate.

3. There is a direct relationship between shot distance and rebound distance. The longer the shot attempt, the further away from the rim the rebound is likely to occur. The corresponds with the idea that 3-point shots often result in “long rebounds”.

4. In the NBA, 3-point shots are much better options than midrange shots for 2 reasons: 1) The decreased FG% is more than compensated by a higher reward in terms of points per attempt, and 2) not only do made 3-point shots obviously result in more points, missed 3-pointers are more likely to result in offensive rebounds than missed midrange jumpshots. Midrange jumpers kill possessions more and result in points less.

The microgeography of missed field goals:

About 65% of the time an NBA player takes a jumper, a future rebound gets its wings. As a result, everytime a shooter rises to take a jump shot, other players begin “fighting for position” – but, where should they fight to get?

First of all, we already know that most rebounds occur near the basket, which is one main justification for the common coaching tenet of boxing out: keep your opponent further away from the rim, and you’ll increase your chance of acquiring a rebound. That may seem obvious, but since the origin of the rebound is almost always a ricochet off some part of the rim/backboard apparatus, and a rebound’s trajectory is generally toward the paint, it makes sense that the person closest to the rim apparatus at the time of the ricochet has the best chance of grabbing the ball.

But positioning wisdom involves more than distance; it involves direction as well.

This concept is best illustrated with baseline shot attempts. Let’s look at the relationship between rebounding locations and shot locations near the baseline. We’ll begin with longish midrange baseline shots. The following image shows where rebounds go when these shots are missed. The yellow highlighted area is the shot zone; the red area is the “rebounding epicenter,” or the area on the court where rebounds are most frequently collected when shots are missed from that shot zone.

As you can see, when an NBA player misses a shot from the baseline, the rebound most frequently occurs on the opposite side of the rim; for visual confirmation, here’s the rebounding signature for baseline shots on the opposite side:

Check out the rebounding epicenter here: when a player misses a longish midrange baseline shot, rebounds are most commonly grabbed at the edge of the “restricted area” on the opposite side of the rim. When we step back to the corner-3 zones, we see the exact same effect – the only difference is that the rebounding epicenter occurs a bit further from the rim… longer shots beget longer rebounds, you guys.

You can see that the rebounding epicenter for missed corner threes is clearly outside the restricted area, and very close to the “low block” on a college basketball court.

Let’s contrast that with some other midrange shots, which result in very different rebounding patterns. When we examine rebounding signatures for shots closer to the middle of the floor we see the epicenter venture back inside the restricted area. The whole “opposite-side-of-the-rim” effect still applies, but is much less drastic; compared to baseline attempts, centralized jump shots beget more centralized rebounding signatures.

Conclusion

Using the information here we can contemplate the confluence of FG%, points per attempt, and offensive rebounding %; we can begin to think about shot selection in the NBA from a more informed plateau. With this in mind, the midrange jumper is the least efficient shot in basketball, it results in the fewest points and also kills possessions at the highest rates. Does this mean midrange shots are always foolish? Of course not, many of the NBA’s best teams like Boston, Miami, and Oklahoma City effectively use the midrange shot on a frequent basis. Regardless, league-wide the efficiency of a shot cannot simply be judged by its expected point total; we must also consider the offensive rebounding rate, which determines whether a given possession ends or whether the offense gets another try. With this in mind, getting shots near the rim has a double-benefit: 1) close shots have a higher FG%, and 2) missed close shots more commonly result in second and third chances for the offense.

I wanted to thank the nice folks at Stats Inc., especially Brian Kopp and Ryan Warkins, for their help with this project. Thanks to SportVu data we can now analyze basketball in exciting new ways. As the NBA enters its own version of the ‘Big Data’ era, we all benefit. Optical tracking data will enable analysts to understand basketball and communicate about basketball in transformative new ways. This data will not only feed the addictions of NBA geeks like me, but they also will help everyone learn a little more about basketball basics. There is an exciting new opportunity for analytics to go beyond helping one team beat another team, but to help the community at-large acquire fundamental knowledge about the game we all love.

13 comments

Most of this isn’t earth-shattering news, but seeing the conventional wisdom visually confirmed like this is pretty damn cool.

The one surprising revelation is that 3-pointers are actually offensively rebounded more often than midrange shots. I always thought that midrange shots got a bum rap for being the least valuable shots, because I figured they were at least more likely to be rebounded by the offense than a 3-pointer. I guess this is a case of data analysis telling us what our eyes and reasoning have misled us into believing.

Still, the fact that 3-pointers do result in long defensive rebounds as well means they probably lead to more fast breaks going the other way, and that’d be an interesting wrinkle to consider when calculating their overall value. Also, you probably get fouled more on midrange shots than on 3-pointers.

Andy, I think I have an explanation for the 3-pointer/midrange rebounding numbers differing from your expectations. About half of rebounds from threes occur outside the restricted area, but most box-outs happen at that line or closer. Essentially, missed threes are so bad they’re good.

To follow up on your post, though, I think you reference the next logical step here. From a given spot on the floor:

- What is the eFG%
- What is the offensive rebound percentage and what is the offense’s PPP on those rebounds
- What is the defensive rebound percentage and what is the defense’s PPP on those rebounds

These five numbers can combine to give you a map of shot expected value that accounts for the probability of scoring or being scored on. And if you substitute an individual player’s eFG% and their team’s rebounding/PPP stats, you can get a map of shot expected value that is specific to that player.

Great breakdown. Reminds me of the 2011 Old Dominion basketball team. They led the nation with a plus 11.9 rebound margin and often rebounded half of their misses. I saw almost every game they played and the offense featured a lot of three point attempts that were quite often missed, but they were always attempted with a rebounder at the weak side. Most three point attempts were from the corner three or wing.

Ironically that team lost on a tap-in to the Butler team that played in the NCAA championship game on a tap in by Matt Howard. The 3rd guy in the rotation failed to get a body on Howard.

It seems obvious that 3-pointers result in more offensive rebounds because they are longer rebounds. The defensive player should be boxing out, which means they are inside of the offensive player. On long rebounds, the ball will fly over the defender’s head because they are usually pushed too far inside.

I disagree with the point that “the midrange jumper is the least efficient shot in basketball.” I think it is less efficient because it is more often times than not, closely contested. You are more likely to be in traffic shooting a mid-range jumper, and a lot of the time it’s a pull-up. A 3-pointer from the corner is usually off a drive and kick, where the defender is inside helping, leading to a more open look.

Thank you for bringing that up, Sam;
I love that paper, but it argues there is little or no relationship between shot direction and rebound location.

My results suggest the opposite.

Here is the key passage from that Sloan Paper:
“One of the interesting results is that there is not discernable bias in terms of [rebound] direction based on shot
location. There are theories that advocate that corner threes tend to be rebounded on the long side of
the shot. We propose that it is not possible to discern which sector is associated with which scatterplot by inspection thus
indicating that there is a consistent uniform distribution of rebound angle and distance.”

IIRC, that paper by Maheswaran et al., analyzed the location of a rebound became “reachable”, that is the location of the ball, the moment the ball is below 8ft, whereas your study uses the actual location the player controlled the rebound (it does, right?).

High rebounds were left out of their analysis, which could explain why “Get Rebound Here” areas you indicate are not found by Maheswaran. Could it be that a significant number of rebounds close to the basket are grabbed high (>8ft) in the NBA?

Another thing is that Maheswaran et al. present a scatter plot with reachable location and (qualitatively) state that rebound from corner shots can not be distinguished. IMO the two middle plots indicate corner shots. Since Maheswaran don’t show the actual shot location for each scatter plot, we can’t check – which makes theirs a false (at least unfounded) claim.

Another interesting thing is the difference between your study: “where the rebound is grabbed” vs Maheswaran et al “where the rebound *could* be grabbed”. If professional ball players are “drilled” to get the rebound on the weak side, one can expect to find that most rebound are grabbed there.

For now I’m not convinced by Maheswaran, because it does not *convincingly* reject “common basketball wisdom – get rebounds on the other side of the basket” (supported by your study).

This is the best website I have ever visited. Excellent work and will definitely visit more often. Its mindblowing how you keep introducing new topics to analyze. I also think NBA teams should have recruit you already, and I hope its the Heat.

Have you tried looking at the location graphs of offensive rebounds compared to defensive rebounds? Will probably just confirm that offensive rebounds happen further from the basket, but it’d be interesting if it doesn’t.

I think another aspect that can be seen in the data is the effect of the dominant hand. As most NBA players like the rest of the population is right handed, it affects the results here. Besides the higher percentages on the right side of the court, it also effects the trajecory of the misses. Even shots straight on from the basket, come off more to the left. Theory, in addition to most often missing long, you most often miss on the same side as your dominat hand.

Thanks again for the interesting article, Prof. Goldsberry. As a fellow geographer and avid basketball fan, it has been great to find your site and the research you are doing (with both basketball and food geographies). I had never thought of using GIS to map basketball stats. So cool… I wish I had come across your stuff when I was in grad school a few years ago and looking for someone’s geography research to follow (now I’m stuck in a job marginally related to the field, lol). Keep up the great work! I’m looking forward to your upcoming research and articles…